some thoughts and comments about the railway track

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Jointed track breathing

Rail breathing

Normally on the railway track the rail is fixed through a set of superstructure elements (fastenings, sleepers, ballast) that opposes the rail tendency to expand or contract due to temperature variations. This fixation is achieved through friction forces and once the rail axial forces are above these friction forces, the rail will start to move relative to the surpassed resistance unless is constrained further at a different level, by another resistance (friction) force.

From this perspective there are two main resistance forces (presented in previous articles):

Jointed track breathing

For jointed track, as long as the rail temperature has not increased enough to generate an axial force that can overcome the joint resistance R, there will be no joint gap variation and potentially no rail displacement.

When the rail temperature has increased relative to the rail installation temperature sufficient enough to overcome the joint resistanceforce R, the rail expansion starts and gradually, sleeper by sleeper and the longitudinal track resistance p will mobilise to oppose the free expansion. When this mobilisation has been achieved on the entire rail length, the rail will further expand freely. This staged and complex behaviour is usually called “rail breathing”.

For jointed track, a normal axial force diagram with all the resistance forces mobilised, can be represented as in the figure below:

Please keep in mind, dear reader, the peak that exists on each rail force diagram, on jointed track.

Considering the two resistance forces, the annual joint gap variation of this jointed track can be represented in a rail temperature/gap diagram:

Compared to the very theoreticalFree Thermal Expansion (FTE) track superstructure, this Restrained Thermal Expansion (RTE) superstructure will develop a hysteresis graph, a delayed response to rail temperature variation. A rail temperature change will not immediately cause a visible rail expansion or contraction and the resistance forces mentioned above will behave as a moderator of the rail response to temperature.

In such a case, closer to the real behaviour of the track, for a given temperature there will be a range of values for the joint gap and not a fixed one. For the entire annual rail temperature variation, this range of values is inscribed in a domain of joint gap variation (see the graph above).

Also during any daily rail temperature circle, the joint gap will have a very complex variation which cannot be predicted only by simple calculations based on the free thermal expansion physical laws (ΔL = αLΔt°) – see the green graph in the figure above, presenting a theoretical joint gap variation for one day.

In railway engineering the rail breathing length is called the rail length involved in the thermal expansion/contraction behaviour. For jointed track this length is usually identical to the rail length and the “breathing length” term is not usually used as such. That is not the case for continuous welded rail (CWR) track, as we will see in the next article.

NB: A funny correlation – the rail joint “breathing” in the figure has a graph similar to a “lung” .